Chessmaster1000: You got it wrong. In the limit, the chance that you roll 5-5 "for ever" goes to zero, that's right. So, the chance for an infinite long game is zero. But that's not the same as an infinite number of games. Here is how it goes:

Take the following position: both players have 13 pieces off. White has its two remaining pieces on his 6 point. Black has its two remaining pieces on white's 5 point. White to roll.

If white rolls 6-6, the game is over. Call this game 1.
For game two, white rolls 1-1 (can't move). Black rolls 1-1 (can't move either). White rolls 6-6. End of game. This is game 2.
For game 3, the sequence goes: white rolls 1-1, black rolls 1-1, white rolls 1-1, black rolls 1-1, white rolls 6-6.
Or more general, for game N, both white and black start with N-1 rolls of 1-1 (this chance is not zero), and then white rolls 6-6.

Say there are a finite number of games, call this number M. But that could not have included a game that reached the position I described above and then continued with M rolls of 1-1 on both sides, followed by a roll of 6-6. Ergo, there's no limit on the number of different games.